George Osborne is under pressure from Conservative MPs to introduce a promised marriage tax allowance to ensure that stay-at-home parents are not penalised by new childcare benefits unveiled by the government on Tuesday.

As a charity warned of a "fresh bout of discrimination" against parents who sacrifice their careers to look after their children, one Tory made an 11th-hour appeal to the chancellor before the budget to solve the problem at a stroke by introducing a transferable tax allowance.

The row broke out after the government announced that a £750m childcare scheme will only be available where both parents are in work, with neither earning more than £150,000.

Parents on joint incomes of up to £300,000 will be eligible to claim 20% of the costs of childcare worth up to £6,000. This will provide help of £1,200 a child per year. Families receiving tax credits or receiving the new universal credit will receive help under a different and more generous scheme.

Liz Truss, the children's minister, rejected claims that the new scheme would disproportionately benefit affluent parents because only the highest rate taxpayers, earning £150,000 and above, will be excluded. She said the new scheme would benefit 2.5m people rather than the 500,000 who benefit from the current Employer Supported Childcare (ESC).

Truss told the BBC: "Everybody who is currently claiming employer vouchers will be able to continue claiming employer vouchers. But we are making the system much fairer because at the moment it is based on household.

"Our system is based on a per-child amount, so if you have two children you get £2,400, three children £3,600. That is much fairer, because we all know childcare costs are related to the number of children and not the number of parents. The scheme is also open much wider, so anybody who is eligible, who is working, can go on to the internet, sign up for an account. It is going to be a very simple process and they can receive that funding.

"At the moment only 500,000 people can claim the employer vouchers. This will be open to 2.5 million people who will be able to sign up for it online – it will be very simple. You pay 80% of the costs, the government pays 20%, up to a maximum of £1,200 per child."

The Treasury faced questions when an internal question and answer document, arguing that working parents "are in greater need", was released accidentally on its website. Under a section headed "key rebuttals" – the language used in Whitehall to help officials answer difficult questions – it answered a mock question about why the scheme was not available to families where one parents stays at home. This is in contrast to ESC.

The document, captured by the Politics Home website before it was withdrawn by the Treasury, said: "We need to focus our resources. Working families who are struggling with their childcare costs or families where parents want to go to work but can't afford to do so are in greater need of state support for childcare than families where one parent chooses to stay at home and look after children full time."

Marie Peacock, chair of the Mothers at Home Matter charity, was highly critical of this thinking. "Britain and Mexico are the only nations in the western world where the family is not recognised as a household unit in the tax system. All other democratic countries provide tax relief for parents wanting to fill the vital role of raising children.

"We want to see a level playing field for childcare. This has to mean tax breaks for families with one earner to compensate for the extra household costs of raising children and to ensure that we end the current sharp discrimination against stay-at-home mothers who choose to make a financial sacrifice to look after their babies and toddlers."

Tory MPs said that Osborne should introduce the marriage tax allowance promised in the Tory manifesto. The Liberal Democrats are fiercely opposed to this measure but the chancellor has the right, under the terms of the coalition agreement, to put it before parliament.

The Lib Dems agreed in the coalition agreement to abstain in any vote on "budget resolutions to introduce transferable tax allowances for married couples". The Tories would be in a strong position to win such a vote because they number 304 in the Commons, against 257 Labour MPs.

Robert Buckland, the Tory MP for Swindon South, said: "The announcement on childcare is welcome and it is addressing people who want to go to work. But there is an equally valid decision by thousands of mums and dads to stay at home. The best way to deal with this is to advance what was the Conservative agenda to have a transferable tax allowance that would benefit the family. The wage earner would have an increased protection and shelter from tax and the family would all benefit as a result."

Buckland added that he was not pushing a traditional agenda because many fathers stay at home. "It is not about being traditional and saying mum must stay at home because many dads very often stay at home now where the mum has a high paid job and wants to go to work."